#!/usr/bin/python
# -*- coding: utf-8 -*-

"""Project Euler Solution 015

Copyright (c) 2011 by Robert Vella - robert.r.h.vella@gmail.com

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""

import cProfile
from euler.numbers.combinatorics import number_of_combinations

def get_answer():
    """Question: 
    
    Starting in the top left corner of a 2×2 grid, there are 6 routes 
    (without backtracking) to the bottom right corner.

    How many routes are there through a 20×20 grid?
    """
    
    #Given that the arrow can only move in the four cardinal directions,
    #then the path will always contain 20 + 20 moves (manhattan distance).
    #Each path will also always contain 20 movements to the right and 
    #20 movements down. In actuality only half of the movements are optional
    #for each path, the the other half are required to reach the end.
    #Therefore, the problem can be phrased as 'Find me all the possible
    #combinations of 20 movements from a set of 40'.    
    return number_of_combinations(40, 20)
    
if __name__ == "__main__":
    cProfile.run("print(get_answer())")
